Maryam Mirzakhani, the Iranian-born mathematician who is the only woman to have won the prestigious mathematics Fields Medal, has died from breast cancer aged 40.

The Stanford University professor in 2014 was one of four recipients of the award, which is presented every four years and is considered the mathematics equivalent of the Nobel Prize.

She was named for her work on complex geometry.

Her highly theoretical work in areas like moduli spaces, Teichmüller theory, and hyperbolic geometry "read like a foreign language" to those outside of maths, a statement from Stanford University said.

"Mastering these approaches allowed Mirzakhani to pursue her fascination for describing the geometric and dynamic complexities of curved surfaces – spheres, doughnut shapes and even amoebas – in as great detail as possible."

Her work, the leading California-based university, added, "could have impacts concerning the theoretical physics of how the universe came to exist".

Born in Tehran, Mirzakhani came of age after the Iran-Iraq war as Iran went through a period of relative social and political calm. She went on to Harvard, before becoming a faculty member at Stanford in 2008, aged just 31.

"The grievous passing of Maryam Mirzakhani, the eminent Iranian and world-renowned mathematician, is very much heart-rending," Iranian President Hassan Rouhani said in a message that was reported by the Tehran Times.

Iran's foreign minister, Mohammad Javad Zarif, sent "heartfelt condolences" to her family, all Iranians, and the scientific community, the newspaper reported.

"The news of young Iranian genius and math professor Maryam Mirzakhani's passing has brought a deep pang of sorrow to me and all Iranians who are proud of their eminent and distinguished scientists," Zarif posted in Farsi on his Instagram account.

Dignitaries and leading scientists took to social media to pay tribute to Mirzakhani, while Iranian newspapers have broken with tradition and featured Mirzakhani on their front-pages without a hijab.

Iranian newspaper Hamshahri is running a front page photo of Mirzakhani tomorrow without a hijab.